Warping of the space-time surface explains the variation of Newton's constant

Esa Ruoho has been studying Allais effect and has sent excellent and very inspiring questions related to the Allais effect. His questions have led to rather detailed and highly predictive TGD based model for the Allais effect based on the notion of warping distinguishing between GRT and TGD.

One of the latest questions whether the predicted large reduction of the light velocity, which is due to warping made possible only for space-times identified as 4-surfaces, could reflect itself in the value of the gravitational constant G.

Indeed, in 2015 a team of researchers led by J. D. Anderson published a study in Europhysics Letters (see this) reporting that measurements of Newton’s gravitational constant G over several decades appear to oscillate with a period of 5.899 +/- 0.062 years. The periodicity in G measurements matches the approximately 5.9-year oscillation found in Length of Day (LOD) variations, which are fluctuations in Earth's rotation rate. This phenomenon would be analogous to the variation of the pendulum period in the Allais effect.

Could warping, which predicts that the speed of light can have values c_# ≤ c=1 (here the units with c=1 are used), relate to the far too large variation associated with G measurements? Warping indeed affects the measured value of G.

I looked more closely to see if warping, which predicts that the speed of light can have values c_#≤c, could explain the far too large variation associated with G measurements. The second possibility is that the variation of the effective value of G is induced by the pressure caused by dark graviton feed from the Sun.

1. Warping does not affect the gradient of the gravitational potential to which the gravitational force is proportional. However, it causes a small change in g_tt and therefore in g^tt.
2. The gravitational acceleration predicted by GRT is given by

   (1- r_{s/r²) ×GM/r²}

   g_tt= 1-GMR/c²r == c_#² and extremely close to value 1 for the solar system.

3. c_#² is transformed by warping:

   g_tt=c_#²→ c_#² -R²×ω² .

   The change of g_tt can be much larger than the very small deviation of g_tt from 1 predicted by GRT. The effect on the gravitational force is however trivial.

Could the radiation pressure of the graviton flux coming from the Sun or from the Earth itself affect the value G_eff of G? This pressure decreases like 1/r² just as the gravitational force does. For the Sun graviton flux would concentrate to the wavelength λ= Λ_gr= 3000 km and the energies of gravitons would vary in the range 1-10⁵ eV. For the Earth the wavelength would be λ=Λ_gr= 5 mm. The period for the variation of c_# should be equal to that for the variation of G is T∼ 5.9 years.

1. If the gravitons with a shared gravitational Compton length λ=Λ_gr∼ R_E/2 from the Sun induce a transversal gravitational force, the variation of G_eff would be basically due to the emission of gravitons. The intensity of the emission of gravitational waves should have T as a period. Sunspot cycle has a period T_S= 11 years (varying in wide limits) and is part of a 22 year cycle. T∼ T_S/2 suggests a chaonic period doubling dynamics.
2. In TGD, sunspots relate very closely to the magnetic monopole flux tubes. The monopole flux loops emitted by reconnection mechanism from the Sun carry solar wind, radiation and also gravitationally dark gravitons with λ=Λ_gr∼ R_E/2 so that frequency-/wavelength resonance amplifies the effect of gravitons. Therefore variation of G_eff would reflect the dynamics of the monopole flux tubes.

   The receival of dark gravitons induces transversal gravitational force and therefore has an effect on the rotation period of the Earth and could explain the correlation with the variation of LOD.

There is a connection to the problem of Hubble tension. The volume action is for warped extremals proportional to c_# and the 14 percent difference of two measured values of Hubble constant.

In the case of the Sun there is a rather dramatic prediction. The value of c_#∼2^-11 for the solar system can apply to gravitational flux tubes. The killer prediction is that signals about various dynamical phenomena in the Sun should appear as doubled. The first signal as ordinary radiation would arrive after 8 min 20 sec and the second copy as dark gravitational radiation after 11 days 20 hours 19 minutes.

See the article Allais effect again or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.